https://file.aiquickdraw.com/mathbot/file/172974399834097dhlu7q.jpg

The problem is asking for the correct graph that represents the system of inequalities:

\[
y - 2x \leq 6, \quad 2x + y \leq 8, \quad x \geq 0, \quad y \geq 0.
\]

Let's analyze each inequality step by step:

1. **First inequality:** \( y - 2x \leq 6 \)  
   Rearranging this gives:
   \[
   y \leq 2x + 6
   \]
   This represents a line with slope 2 and y-intercept 6. The shaded region should be below this line.

2. **Second inequality:** \( 2x + y \leq 8 \)  
   Rearranging this gives:
   \[
   y \leq -2x + 8
   \]
   This represents a line with slope -2 and y-intercept 8. The shaded region should be below this line as well.

3. **Third and fourth inequalities:** \( x \geq 0 \) and \( y \geq 0 \)  
   These indicate that the solution is restricted to the first quadrant.

### Intersection of these inequalities:
We are looking for the region that satisfies all these conditions, which would be the area of overlap of the regions defined by these lines and the quadrant restrictions.

### Observing the graphs:
- In option **a**, the shaded area is located in the first quadrant and below both lines, which seems consistent with the system of inequalities.
- Option **b** does not appear to have the correct shading relative to the inequalities.
- Option **c** has a shaded area in the incorrect region.
- Option **d** and **e** also have shading that does not fit the inequalities.

### Conclusion:
The correct graph is **option a**, where the shaded region is in the first quadrant and satisfies all the inequalities.

Would you like further details on the calculations or explanations?

Here are 5 related questions to expand your understanding:
1. How do you determine the slope and intercept of a linear inequality from its equation?
2. What are the steps to graph multiple inequalities on the same plane?
3. How do you test a point to see if it satisfies a system of inequalities?
4. Why are the restrictions \(x \geq 0\) and \(y \geq 0\) important in this problem?
5. How would the solution region change if one of the inequalities were strict (i.e., \(<\) instead of \(\leq\))?

**Tip:** Always test a point within the shaded region to ensure it satisfies all inequalities.

Grafik yang benar untuk sistem pertidaksamaan y - 2x ≤ 6, 2x + y ≤ 8, x ≥ 0, y ≥ 0 adalah ....

Learn how to solve a system of linear inequalities with a detailed graphical solution. The problem involves shading regions for y - 2x ≤ 6, 2x + y ≤ 8, and quadrant restrictions (x ≥ 0, y ≥ 0). Suitable for students in Grades 10-12.

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